1. Field of the Invention
The present invention relates to launch vehicles for air launching sub-microsatellites, and particularly to a computerized particle swarm-based micro air launch vehicle trajectory optimization method that computes an air launch trajectory that optimizes the payload mass.
2. Description of the Related Art
The demand for sub-microsatellites is growing rapidly, mainly due to the continuously increasing sophistication and decreasing size of microelectronic devices. Currently a half palm-size multi-function device, such as an iPhone® (iPhone is a registered trademark of Apple Inc. of Cupertino, Calif.), can do seamlessly as many functions as a truck full of computers and communication systems did twenty years ago. Since sub-microsatellites are normally launched as a secondary payload to a larger satellite or in a group of sub-microsatellites, they are subject to many mission constraints, such as launch time and insertion orbit. To avoid such constraints, many countries with advanced or advancing space technology are focusing on developing launch systems specifically designed and built for this category of satellites. Ambitious countries that lack the necessary infrastructure for ground launching may also benefit from this emerging space technology.
Therefore, a new method capable of launching the nanosat individually via low cost launching from an airborne platform can be a solution. By implementing air launching, there would be no restrictions on the launch sites, the launch angle and the launch direction. This can be a very strong point, especially to the countries where satellite launching is very difficult owing to geographical reasons. Moreover, “air launch” is a very economical way of launching satellites compared with the ground-launch method, because it can utilize the high initial launching speed from the mother plane, and the improved thrust efficiency resulting from low dynamic pressure and a big nozzle expansion ratio at high altitude.
Launch vehicle design is one of the very interesting applications of multidisciplinary optimization methods where the interdependence between the trajectory and vehicle design is unavoidable. The launch vehicle itself is comprised of several disciplines, which are mainly the mass characteristics, propulsion system, aerodynamic design, and flight dynamics. Each of these disciplines of design has its impact on the vehicle trajectory and launching capacity. Many researchers have studied the design optimization problem of ground-launch vehicles with trajectory optimization being the core optimization objective. A few studies have focused on the design optimization of air-launch vehicles.
A study on miniature launch vehicles has shown that downsizing of the launch vehicle inversely affects the payload fraction of the launch vehicle (payload to total mass ratio) components. It was assumed that the avionics and the attitude control system do not scale according to the cubic scaling law. As a result, a half-size Pegasus weighing about 2,384 kg would only be capable of placing a 7.9-kg payload in low earth orbit (LEO), and a half-size Pegasus XL weighing about 2,951 kg would only be capable of placing a 25.8-kg payload in LEO. In a more recent study a multidisciplinary design optimization has been performed to develop a miniature air-launch system. The study group designed an 850-kg air-launch system, which has a payload capacity of 3.25 kg. This results in payload fraction of about 0.0038, which is much lower than the Pegasus payload fraction (˜0.018).
Particle swarm optimization (PSO) is a population-based stochastic optimization technique, which is inspired by social behavior of bird flocking, or fish schooling. PSO shares many similarities with evolutionary computation techniques, such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators, such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. Compared to GA, the advantages of PSO are that PSO is easy to implement and there are few parameters to adjust.
Moreover, PSO, like all evolutionary algorithms, optimizes a performance index based on input/output relationships only. Therefore, minimal knowledge of the plant under investigation is required. In addition, because derivative information is not needed in the execution of the algorithm, many pitfalls that gradient search methods suffer from can be overcome. It would be desirable to perform trajectory optimization of a Micro Air Launch Vehicle (MALV) using a particle swarm optimization method.
Thus, a particle swarm-based micro air launch vehicle trajectory optimization method solving the aforementioned problems is desired.